Question: Why does AC current change through a transformer?

Hello physics friends! I have a question about AC current I hope you can help me understand. So I know that putting AC through a transformer will raise or lower the voltage, but because power has to be kept constant, the current changes in the opposite direction. But according to Ohm's law, the current is directly proportional to the voltage, so if the voltage goes up, the current goes up. These two things seem to contradict each other.

Also, how would you calculate the output current, taking into account the resistance? I feel like I'm missing some essential component of AC theory, but I haven't been able to figure out what it is. Thank you!

(ﾉ◕ヮ◕)ﾉ*:・ﾟ✧